In this paper, we present highly accurate numerical results for the lowest four energy eigenvalues
of the quartic, sextic and octic anharmonic oscillators over a wide range of the anharmonicity
parameter ##IMG## [http://ej.iop.org/images/0143-0807/36/3/035025/ejp510005ieqn1.gif] {$lambda .$}
Also, we provide illustrative graphs describing the dependence of the eigenvalues on ##IMG##
[http://ej.iop.org/images/0143-0807/36/3/035025/ejp510005ieqn2.gif] {$lambda .$} Our computation is
carried out by using higher-order finite-difference approximation, involving the nine-and-ten-point
differentiation formulas. In addition, we apply Richardson’s extrapolation method in our calculation
for the purpose of achieving a maximum numerical precision. The main advantage of utilizing the
finite-difference approach lies in its simplicity and capability to transform the time-independent
Schrödinger equation into an eigenvalue matrix equation. This allo…